One ballpark estimate of the memory capacity of the human brain is that it is in the range of 10^13 - 10^17 bits (Tipler, 1995). These numbers are much too large for current purposes if we assume that not all of the brain’s memory is in the service of concepts. A smaller number may be arrived at by assuming that concepts are restricted to pre-frontal cortex (PFC). The volume percentage of PFC to the whole brain is 12.51 (McBride, Arnold, & Gur, 1999) and thus we arrive at a reduced memory capacity estimate in the ballpark of 10^12 bits.
Is what Mary knows while staring at red for the first time simply too much information than can be squeezed into a memory store of 10^12 bits? It seems not.
An early estimate of the bandwidth of the human eye for color vision is 4.32 x 10^7 bits/sec (Jacobson, 1950, 1951). A more recent estimate is 10^6 bits/sec (Koch et al., 2006) aka a megabyte per second (1MB/sec). The computer-savvy reader may already have an intuitive grasp of 1MB/sec. The Wikipedia entry for “megabyte” (accessed July 24, 2008) tells us that a megabyte of data is roughly equivalent to a 1024x1024 pixel bitmap image with 256 colors (8 bpp color depth), 1 minute of 128 kbit/s MP3 compressed music, or a typical book volume in text format (500 pages × 2000 characters).
Assuming Mary has to stare at a red object for a full second to know what it’s like to see red, our lowest estimate of human memory capacity is still an order of magnitude higher than what comes into her eye during that second. (And that’s assuming that Mary has a normal-sized human PFC. Physically omniscient Mary may likely have a bigger brain than normal.) From a purely information-theoretic perspective, giving her bigger lobes would make it even easier to know what it’s like.
So, from an information-theoretic perspective, Mary’s memory capacity is easily large enough for phenomenal knowledge to be conceptual. But the information has to get in there somehow and maybe color vision is the only pipeline fat enough to do the trick. Unfortunately for the defender of the Experience Requirement, there’s no purely information theoretic basis for her position.
Jacobson (1950, 1951) gives a bandwidth estimate of 4.32 x 10^6 bits/sec for the eye for black and white vision and an estimate of 9,900 bits/sec for the bandwidth of the human ear. Continuing with our assumption that Mary would require a full second to gain, via color vision, knowledge of what it’s like to see red, then the very same amount of information can be acquired by a color blind person in 10 seconds and a blind person acquiring the information auditorially would need a full 73 minutes. Reducing our estimate of how long Mary needs to a tenth of a second means that the color blind could acquire that information in about a second and the fully blind in seven minutes.
(Of course, none of this is to say that, for example, the blind person would be hearing red. But it is to say that she is learning whatever is to be learned by the sighted when they see red. The information acquired about red may enter sensory systems without giving rise to conscious experience.)
The above considerations about bandwidth help us to see why the Experience Requirement may strike so many people as plausible. There is a marked difference between what you can learn in a second and what you can learn in 73 minutes. And it is reasonable to assume that people have an at least rough grasp of the informational capacities of their various sensory systems.
Nonetheless, regardless of whether we interpret Hume’s assertion about what the blind can know about color as a claim about nomological, metaphysical, or logical possibility, the claim receives no support from these information-theoretic considerations. From the information-theoretic perspective it is nowhere near impossible for the blind to acquire information of the presence of redness. They just need a longer time than the sighted to do so.